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Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t(More)
For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all Yao graphs, with the sole exception of Y5, whether or not they are geometric spanners. In this paper we(More)
We introduce the problem of <i>shape replication</i> in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model(More)
In this paper we propose a novel algorithm that, given a source robot S and a target robot T , reconfigures S into T. Both S and T are robots composed of n atoms arranged in 2 × 2 × 2 meta-modules. The reconfiguration involves a total of O(n) atom operations (expand, contract, attach, detach) and is performed in O(n) parallel steps. This improves on(More)